Oklahoma Republican Senator Tom Coburn, meanwhile, says the White House is exaggerating, and painful or not the cuts must happen.

Politically, some analysts think Republicans have more to lose.

"The more people see services disrupted, just as you would in a government shutdown which is more dramatic, the more likely it is you'll get Republicans to bend," says CNBC Chief Washington Correspondent John Harwood.

Right now there's no sense if any serious compromise is in the works, with just four days left and counting.